There was a cutscene in which the Player Character is doing a ridiculous dance with Sisipu.
The opening wagon-ride into Gridania in A Realm Reborn has the player seeing some Moogles (in this universe, they appear only to select people), who greet you with adorable horn-toots that only you can hear, and then while talking, one downs the drink of another passenger on the wagon.
Biggs and Wedge make an appearance when you join a Grand Company in ARR. Their comedy duo nature is enhanced even further by them being a Roegadyn and a Lalafell.
Later in the story: You hijack a Magitek Armor. In order to pilot it, the Lalafell is picked up by the Roegadyn, flung around 15 feet into the air, does a flip in the air, and lands in the pilot seat
The Scions of the Seventh Dawn (nee the Circle of Knowing) have a sort of clerk/receptionist who watches the front of their pad in Vesper Bay. She's a Lalafell... named Tataru. And she even does the "taru panic" during one particular cutscene.
During the weaver quests, the quest to learn to socket materia involves an aristocrat who had decided to take up gladiatorial combat. In order to "release his martial potential", he has you craft a cotton acton. However, it mustn't be any old acton like the peasants wear, it must be materia enhanced. When the guildmaster hears the request, he suggests you put in any old piece of materia, as the client likely won't be able to tell the difference.
After completing the request, the guildmaster informs you of an important fact about being a weaver: "While we are not required to respect our clients, we must appear to be respecting their wishes." Furthermore, he declares that you did an excellent job, since "as that little turd was sauntering out of here, I almost mistook him for a gladiator".
After the defeat of Ifrit, emissaries of the Three Grand Companies come to try to court the Player Character to join them, with Minfilia and Tataru both showing signs of exasperation, and even the PC has an expression at one point that just screams "You Have Got to Be Kidding Me!."
Trying to get info on how to fight Titan, you find a man claiming to be a member of a band of mercenaries famous for accomplishing said feat. He turns out to be lying, trying to coast on their reputation, and uses it to get you to do his job. When he's found out, his boss decides to settle the matter by having the two of you compete to see who can destroy a large boulder first. And of course, yours is three times as big as his. And he still cheats. The whole situation is just ridiculous. However that doesn't change the fact the things he does to cheat come back as actual mechanics when you actually do face Titan.
Later he comes back in Patch 2.2 claiming to have defeated Leviabeetus (read; Leviathan) in a previous encounter. He gets a Maelstrom Private going for a while before you show up and he essentially replays a scene from True Lies complete with the comment about his size.
Later, when you actually find one of the actual ex-members of the Band of Heroes, they want to test you, too. They've got a better reason, since challenging Titan just gives the Primal more prayer fuel, but the whole god about to attack Limsa Limosa thing is a bit pressing. Y'shtola's reaction echoes the player's.
Lady Lilira the Lalafel. She acts like an adorably precocious child. And complains about being 'passed around like a swaddled babe'.
I meant the Sultana Nanamo...
One of the Marauder quests. The guildmaster sends you (along with his sister, a conjurer who has already backed you up before) to clear out a nest of beasts as a sort of training exercise. You finish it easily and the conjurer wonders if that was supposed to be a challenge - then you're challenged by a mysterious band of warriors. Actually, they're the guildmaster and several other unnamed guildmates who are all wearing face-concealing helmets. The conjurer says what the player is almost certainly thinking.
Solkwyb: What a ridiculous charade. Did he honestly think we couldn't see through those paltry disguises? [...] Oh, and as a favor to me? Pray indulge Wyrnzoen in his little deception - subterfuge is not a marauder's forte.
And after you report back to the guild:
Wyrnzoen: You did well to to topple opponents of such formidable skill. But let us not dwell on the nature of those masked men. What is important is your triumph in the face of overwhelming odds.
The Dragon Quest X crossover storyline referenced the Dragon Quest"Puff-Puff"Running Gag as your character's 'reward' for completing it. As usual, your character is asked to close his/her eyes as they give you your 'reward'. At the end of it, you open your eyes to catch a face full of a furry/feathery creature being held by the ladies.
Shantotto is specifically compared to The Calamity, in terms of danger to Eorzea. Shantotto is also slightly smaller than a typical Lalafell. And then she brings out Five V... and a rhyme.
Hildibrand returns in usual fashion, digging himself out of his own grave, convinced he's a zombie because of his amnesia. His quest chain is silly, nonsensical, and ends in a way that might leave you flabbergasted by how crazy it is. At one point, Hildibrand makes a joyful face that stretches his model so much it's very obviously meant to push the Uncanny Valley. Hildibrand's teeth also sparkles in the light every time he smiles!
Gilgamesh's exit after his boss battle by attempting to fly away on a rooster leaves the player character so flabbergasted they forget to preform their victory pose with the rest of the party.
The fight against Gilgamesh is also beyond silly; as a nod to his character, Gilgamesh will fake defeat halfway through the first round and then says he lied, proceeding to attack one random player as he buffs himself. Gilgamesh then runs away, saying he "remembered he had something to do" while he drops a bomb behind as another ambush attack. Gilgamesh also can cause Minimum, Toad, and Confusion, which makes the fight look even sillier as shrunk down and frog transformed party members are running around trying to avoid being hit while confused party members attack each other.
Gets Extra silly if the confused members are casters, (And even more so if they're Arcanists/Summoners/Scholars). Ever see Summoner smack a Black Mage repeatedly in the face with a book while the also confused Black Mage smacks the Summoner with their staff?
Once Leviathan has been defeated Thancred can be seen at the counter of The Rising Stones with a bottle of alcohol in his hand spilling his guts to F'lhaminn, who he's been crushing on ever since she resurfaced in 2.1. Topics include the first time he ever saw her, how pretty she is, and how he's been pretty crazy for her ever since. She seems flattered enough but decides it's time he stops drinking.
Upon moving to the Rising Stones, a Roegadyn by the name of Hoary Boulder joins the Scions as a minor NPC, while he's only there to give some life to the Scions' HQ, nearly every time you see him between quests, he's engaged in some minor comic relief, from being beaten up by Yda to overzealously training the Doman children.
Patch 2.3 and Hildibrand again. Nashu brings some more of her explosives along for some reason, and leaves them on a crate of fruit, and starts to (poorly) take notes of what her boss Hildebrand is saying for the record. A series of events causes all of these to fall into place when rival inspector Biraidan comes back from questioning a victim of the Phantom Thief, and leads to this.